Ultra Feller operators from a functional analytic perspective
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917717008711680 |
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| author | Dobrick, Alexander Hölz, Julian Kunze, Markus |
| author_facet | Dobrick, Alexander Hölz, Julian Kunze, Markus |
| contents | It is a widely acknowledged fact that the product of two positive strong Feller operators on a Polish space $E$ enjoys the ultra Feller property. We present a functional analytic proof of this fact that allows us to drop the assumption that the operators are positive and also extends the applicability of this result to more general state spaces. As it turns out, this result can be considered a variant of the theorem that on a Banach space with the Dunford--Pettis property, the product of two weakly compact operators is compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ultra Feller operators from a functional analytic perspective Dobrick, Alexander Hölz, Julian Kunze, Markus Functional Analysis Probability 46A50, 47B07 It is a widely acknowledged fact that the product of two positive strong Feller operators on a Polish space $E$ enjoys the ultra Feller property. We present a functional analytic proof of this fact that allows us to drop the assumption that the operators are positive and also extends the applicability of this result to more general state spaces. As it turns out, this result can be considered a variant of the theorem that on a Banach space with the Dunford--Pettis property, the product of two weakly compact operators is compact. |
| title | Ultra Feller operators from a functional analytic perspective |
| topic | Functional Analysis Probability 46A50, 47B07 |
| url | https://arxiv.org/abs/2312.13266 |